Groups with Only the Identity Fixing Three Letters

Citation

Keller, Gordon Ernest (1965) Groups with Only the Identity Fixing Three Letters. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/GVHG-EC49. https://resolver.caltech.edu/CaltechETD:etd-04142003-092438

Abstract

In this paper, we study finite transitive permutation groups in which only the identity fixes as many as three letters, and in which the subgroup fixing a letter is self normalizing. If G is such a group, the principal results concern the case when G is simple. In this case, H, the subgroup fixing a letter, is a Frobenius group, MQ, with kernel M and complement Q. If |H| is even we show that either G is doubly transitive or permutation isomorphic to the representation of A[subscript 5] on ten letters. If |H| is odd we prove that Q is cyclic, M is a p-group, and G has a single class of involutions. Furthermore, the number of groups for which H has a given positive number of regular orbits is finite.

Thesis Files